Question

If A=−5i+6j−3k and B=3i+4j+2k, determine (A×B)

Answer 1

To find the cross product A × B for vectors A = -5i + 6j - 3k and B = 3i + 4j + 2k, use the formula (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k. It results in 24i + j - 38k.

Step-by-step explanation:

The student is asking how to determine the cross product of two vectors, A and B. The cross product (also known as the vector product) is a binary operation on two vectors in three-dimensional space. Given the vectors A = -5i + 6j - 3k and B = 3i + 4j + 2k, the cross product A × B can be calculated using the following formula:

1. Component-wise multiplication and subtraction, based on the unit vectors i, j, and k.
2. Combining like terms to simplify the expression.
3. Factoring out the common unit vectors i, j, and k.

This yields the cross product: (A × B) = (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k = (6 × 2 - (-3) × 4)i + ((-3) × 3 - (-5) × 2)j + ((-5) × 4 - 6 × 3)k = (12 + 12)i + (-9 + 10)j + (-20 - 18)k = 24i + j - 38k.